1

Improved Howland Current Pump Stability

Tim GreenSenior Analog Applications EngineersPrecision Analog Linear Applications

July 19, 2013

2

Improved Howland Current PumpIL Accuracy Circuit

RS 5

RF 5kRI 1k

RZ 1k

RX 5k

RL

10

VO

VL

VM 100m

VP 200m

-

+

-

+VCV1

RT 0

A+

IL

X1G

RT allows for trim to optimum ZOUT and improved DC Accuracy

IL

VPRX

RZ

RF

RI1

RS

RZ

VMRF

RI

RX

RZ1

RS

RL1

RX

RZ

RS RXRZ

RF

RI

RL

Ideal Op Amp

3

Improved Howland Current PumpV-I DC Accuracy Calculations

1% Resistors (w/RT=0) could yield only 9% Accuracy at T=25°C

Still useful for V-I control in Motors/Valves V-Torque ControlOuter position feedback adjusts V for final position

RT RF RX RI RZ RS RL IL VL VOAM1 Sensitivity

(%) Comments2.858407 5000 5000 1000 1000 5 10 0.100000052 1.000000100 1.500667000 0.000000000 Rt adjusted for Ideal IL

0 5000 5000 1000 1000 5 10 0.099866893 0.998668931 1.498669000 0.133158931 Rt=0, Nominal Values2.858407 5050 5000 1000 1000 5 10 0.102371216 1.023712000 1.536255000 -2.371162767 1% Resistor Changes2.858407 5000 5050 1000 1000 5 10 0.098700599 0.987005991 1.481159000 1.299452324 1% Resistor Changes2.858407 5000 5000 1010 1000 5 10 0.097727653 0.977276527 1.466563000 2.272397818 1% Resistor Changes2.858407 5000 5000 1000 1010 5 10 0.101353602 1.013536000 1.520981000 -1.353549296 1% Resistor Changes2.858407 5000 5000 1000 1000 5.05 10 0.099009365 0.990094651 1.490756000 0.990686485 1% Resistor Changes2.858407 5000 5000 1000 1000 5 10.1 0.099999329 1.009993000 1.510665000 0.000723 1% Resistor Changes

0 5050 4950 990 1010 4.95 10 0.108995522 1.089955000 1.630222000 -8.995465322 1% Worst Case w/RT=0)2.858407 5050 4950 990 1010 4.95 10 0.109152449 1.091524000 1.632570000 -9.152392241 1% Worst Case w/RT=Nom)

4

Improved Howland Current PumpSimplified Equation

RS 5

RF 5k

RI 1k

RI 1k

RF 5k

RL 3

VO

VLVM 100m

VP 200m

Vs+ 5

+

-

+

Iset

En

Imon IflagIflag

Tflag

U1 OPA569

Rse

t 5

.76

k

R4

50

0k

R3

50

0k

R5

50

0k

LL 30m

A+

IL

Assume:RF = RXRI = RZRF>>RSRF>>RL

IL

VP VM( )RF

RI

RS

5

RS 5

RF 5k

RI 1k

RZ 1k

RX 5k

RL 3

VO

VLVM 100m

VP 200m

Vs+ 5

+

-

+

Iset

En

Imon IflagIflag

Tflag

U1 OPA569

Rse

t 5.7

6k

R4

500

k

R3

500

k

R5

500

k

LL 30m

A+

IL

-

+

Improved Howland AC Analysis

Op Amp sees differential [(-IN) – (+IN)] feedback = - - + (Must be positive number else oscillation!)

RF

RI

6

Improved Howland AC Analysis

+

Aol VOUT

1/ = 1 (-) - (+)

+

-

7

Improved Howland 1/ Plot - Full Load

1 10 100 1K 10K 100K 1M 10M

Frequency (Hz)

Gai

n (d

B)

0

20

40

60

80

100

120

OPA569 Aol

fz44.08Hz

fp31.83kHz

1/RO=Full Load

STABLE

8

Improved Howland 1/ CalculationNo Load & Full Load

IL RO fz fp DC 1/ Hi-f 1/

No Load 0A 6.29 75.8Hz 31.83kHz 17.62dB 77.17dB

Full Load 1A 0.308 44.08Hz 31.83kHz 19.45dB 77.15dB

Change in RO from No Load to Full Load has no significant impact on the 1/ Plot

9

Improved Howland Tina Transient Analysis Circuit

RS 5

RF 5k

RI 1k

RZ 1k

RX 5k

RL 3

VO

VL

VP 500m

Vs+ 5

+

-

+

Iset

En

Imon IflagIflag

Tflag

U1 OPA569

Rse

t 5

.76

k

R4

50

0k

R3

50

0k

R5

50

0k

LL 30m

A+

IL

+VG2

+/-10mV

100Hz

RF

RI

10

Improved Howland Tina Transient Analysis Results

T

Time (s)

0.00 5.00m 10.00m 15.00m 20.00m

IL

476.55m

514.33m

VG2

-10.00m

10.00m

VL

-2.94

2.57

VO

-414.75m

4.97

STABLE

11

Improved HowlandModified 1/ for Stability

1 10 100 1K 10K 100K 1M 10M

Frequency (Hz)

Gai

n (d

B)

0

20

40

60

80

100

120

OPA569 Aol

fz44.08Hz

fp31.83kHz

1/RO=Full Load

+ FB#2 toModify 1/

Modified 1/

fz1

12

Improved Howland AC AnalysisFinal Design for Stability

RS 5

RF 5k

RI 1k

RZ 1k

RX 5k

RL 3

VO

VLVM 100m

VP 200m

Vs+ 5

+

-

+

Iset

En

Imon IflagIflag

Tflag

U1 OPA569R

set

5.7

6k

R4

50

0k

R3

50

0k

R5

50

0k

LL 30m

A+

IL

RO 309m

-

+

-

+VCV1LT 1G

CT 1G

VT

+

VG1

VOA

VM

VP

V+

Vbeta

Rd

13

kC

f 2

70

nAol = VO/Vbeta

1/Beta = VT/Vbeta

Loop Gain = VO/VT RO = 6.29 No Load

RO = 0.308 Full Load

RF

RI

13

Improved Howland AC Analysis1/ - Final Design for Stability

T

OPA569 Aol

1/Beta

Frequency (Hz)

1 10 100 1k 10k 100k 1M 10M

Ga

in (

dB

)

-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

120.00

OPA569 Aol

Aol A:(43.22; 89.66) B:(417.02; 69.97) Beta1 A:(43.22; 23.15) B:(417.02; 37.01)

1/Beta

a b

fcl

14

Improved Howland AC AnalysisLoop Gain - Final Design for Stability

T

Loop Gain

Loop Gain

Frequency (Hz)

1 10 100 1k 10k 100k 1M 10M

Ga

in (

dB

)

-80.00

-60.00

-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

120.00

Frequency (Hz)

1 10 100 1k 10k 100k 1M 10M

Ph

ase

[de

g]

-45.00

0.00

45.00

90.00

Gain : Loop A:(13.43k; -38.44m)

Phase : Loop A:(13.43k; 87.84)

Loop Gain

Loop Gain

a

fcl

15

RS 5

RF 5k

RI 1k

RZ 1k

RX 5k

RL 3

VO

VL

VP 500m

Vs+ 5

+

-

+

Iset

En

Imon IflagIflag

Tflag

U1 OPA569

Rse

t 5

.76

k

R4

50

0k

R3

50

0k

R5

50

0k

LL 30m

A+

IL

+

VIN

Rd

13

kC

d 2

70

n

Improved Howland AC Transfer AnalysisIL/VIN - Final Design for Stability

RF

RI

16

Improved Howland AC Transfer AnalysisIL/VIN - Final Design for Stability

T

IL/VIN

IL/VIN

Frequency (Hz)

1 10 100 1k 10k 100k 1M 10M

Ga

in (

dB

)

-140.00

-120.00

-100.00

-80.00

-60.00

-40.00

-20.00

0.00

20.00

Frequency (Hz)

1 10 100 1k 10k 100k 1M 10M

Ph

ase

[de

g]

-90.00

-45.00

0.00

45.00

90.00

135.00

180.00

Gain : IL A:(393.63; -2.18)

Phase : IL A:(393.63; 135.34)

IL/VIN

IL/VIN

a

17

Improved Howland Transient AnalysisIL/VIN - Final Design for Stability

RS 5

RF 5k

RI 1k

RZ 1k

RX 5k

RL 3

VO

VL

VP 500m

Vs+ 5

+

-

+

Iset

En

Imon IflagIflag

Tflag

U1 OPA569

Rse

t 5

.76

k

R4

50

0k

R3

50

0k

R5

50

0k

LL 30m

A+

IL

+VIN

Rd

13

kC

f 2

70

n

+/-10mV

100Hz

RF

RI

18

Improved Howland Transient AnalysisIL/VIN - Final Design for Stability

T

Time (s)

0.00 5.00m 10.00m 15.00m 20.00m

IL

489.03m

510.68m

VIN

-10.00m

10.00m

VL

12.44m

2.50

VO

2.55

4.96